President Trump at a fundraiser in North Carolina last week.CreditCreditT.J. Kirkpatrick for The New York Times

President Trump and the Koch brothers have made it clear that they don’t like each other. Politically speaking, they are in fundamental disagreement over trade, tariffs and immigration.

Nonetheless, there is a functional Trump-Koch alliance, and the Republican Party has capitalized handsomely on it. Trump’s racially freighted, anti-immigrant rhetoric has been essential to persuading white voters to agree to Republicans’ long-sought tax and regulatory policies. These policies are inimical or irrelevant to the interests of low- and moderate-income Americans. They have been promulgated by the Trump administration, but many of them have been meticulously prepared and packaged by the Kochs’ massive political network.

A 2014 Washington Post story described the Koch political empire as a “labyrinth of tax-exempt groups and limited-liability companies” designed to “mask the sources of the money.” Much of this money continues to go to voter mobilization and television ads and financing the construction and maintenance of some of the most sophisticated and detailed voter lists anywhere.

The Koch network — which in many respects has eclipsed the official Republican Party — has nurtured the careers of a host of politicians from Mike Pence to Scott Walker to Mike Pompeo. Major beneficiaries of the Koch network include the Tea Party, the Cato Institute, the National Federation of Independent Business and groups specifically created to act as conservative counterweights to a panoply of liberal interest groups — for example, the 60 Plus Association and the Center to Protect Patient Rights are conservative alternatives to the AARP.

The Kochs’ policy objectives that have been realized since Trump took office are legion: enactment of the $1.5 trillion tax cut; the opening of public lands to mining; the appointment of men and women with industry ties to key regulatory posts; weakened enforcement of worker safety rules; the proposed elimination or rollback of numerous environmental regulations; the appointment of Neil Gorsuch to the Supreme Court, along with the nomination of Brett Kavanaugh, and the appointment of judges favored by the Kochs to all levels of the federal bench.

In this context, the public disagreement between Trump and Koch over trade, tariffs and even immigration clearly diminishes in importance.

At a July gathering of Koch network donors in Colorado Springs, Charles Koch took a conciliatory approach when speaking specifically about Trump. Asked if Trump was to blame for heightened national divisiveness, Koch replied:

We’re all part of it. None of us are perfect. We’ve had divisiveness long before Trump became president, and we’ll have it long after he’s no longer president. I’m into hating the sin, not the sinner.

Koch also told donors, “We’ve made more progress in the past five years than I’ve made in the previous 50.”

Trump and the Kochs are not just complementary; they are symbiotic. Trump is essential to marketing the Kochs’ vision. Without him, the Koch agenda would fail.

Any realistic assessment of the policy victories achieved by the Kochs shows that the public is firmly opposed to much of what the Kochs have gained from the Trump administration and a pliant Congress — and the public is opposed to much of what the Kochs still want and have not yet achieved.

An April 2017 Gallup poll, conducted as Congress began consideration of the Koch-backed tax bill (which was passed in December) found that 63 percent of voters believed that the rich paid too little in taxes and 67 percent believed that corporations paid too little. In other words, they were directly opposed to what the bill actually did.

Similarly, a Reuters/IPSOS poll earlier that year found that 61 percent of voters wanted Environmental Protection Agency regulations either strengthened (39 percent) or maintained (22 percent). Nineteen percent backed weakening E.P.A. rules — a prime objective of the Kochs, much of whose wealth derives from the petroleum and chemical industries.

If public opinion were the guiding force, key elements of the Kochs’ policy goals would be dead in the water. And without Trump’s ethnonationalist appeal, these proposals (for the most part) would not survive either on their merits or on popular support.

Put another way, the Charles Koch-Donald Trump collaboration has been productive, despite the distaste of the two men for each other.

Asked during the 2016 campaign how he would vote, Charles Koch demurred, “If I had to vote for cancer or a heart attack, why would I vote for either?”

Trump, in turn, described the Koch brothers in two July 31 tweets as “a total joke in real Republican circles” whose motives were “to protect their companies outside the U.S. from being taxed.”

This war of words, however, is of only peripheral importance.

“Recently we have seen a much overhyped supposed split between Koch and the network and the Trump administration around free trade questions,” Theda Skocpol, a professor of government and sociology at Harvard, said by email. “This is mostly sound and fury with little impact.”

In practice, Skocpol wrote,

The Koch network has gotten 85 percent of what it has always wanted out of the Trump presidency so far — especially the huge government-starving, upward tilted tax cuts, the evisceration of the EPA, weakening of labor regulations and unions, cuts in social spending, and ultraright judges who will eviscerate government regulatory capacities and further weaken liberal forces.

In 2016, according to Bruce Cain, a political scientist at Stanford, Trump was crucial to bridging the gap between his followers — “protectionist, anti-elite elements that are skeptical of globalization and free trade” — and free-trade conservatives.

Alexander Hertel-Fernandez, a political scientist at Columbia, made a parallel point:

On most issues the Trump administration, working together with a Republican Congress the Kochs helped to elect, has embraced the vision of the Republican Party that the Kochs have pursued aggressively over the past three decades. That includes implementing massive cuts to taxes, especially on businesses; dismantling the Affordable Care Act; appointing very conservative, free-market oriented judges to the federal judiciary; and efforts to undermine economic and environmental regulations.

Hertel-Fernandez noted that

trade and immigration are, to be sure, a point of disagreement between the Kochs and the Trump administration, but those are still only two areas where the Kochs have not gotten their way among many other successes.

No issue is more important to the continuing strength of the Koch network than campaign finance — Koch-aligned organizations were instrumental in successfully pressing the case that resulted in the key 2010 Supreme Court decision Citizens United — and the Trump administration’s judicial nominees are virtually certain to secure, if not broaden, the legal protections crucial to the Kochs.

Much of the multimillion dollar Koch empire is built on donor anonymity based on the use of tax-exempt organizations that do not have to publicly report contributors. (The Koch family has, of course, made many donations in its own name.)

In a 2015 story, Confessore reported that the Koch brothers planned “to spend close to $900 million on the 2016 campaign, an unparalleled effort by coordinated outside groups to shape a presidential election.” The Kochs, Confessore continued,

are longtime opponents of campaign disclosure laws. Unlike the parties, their network is constructed chiefly of nonprofit groups that are not required to reveal donors. That makes it almost impossible to tell how much of the money is provided by the Kochs — among the wealthiest men in the country — and how much by other donors.

In a 2014 District of Columbia federal court case in which Americans for Prosperity successfully challenged the California Attorney General’s attempts to require disclosure of donors, Derek Shaffer, a lawyer for A.F.P., a Koch group, argued that contributors could be subject to harassment, just as civil rights supporters were in the 1950s South:

For some 50 years, Your Honor, since the Supreme Court in 1958 upheld the right of the NAACP to resist compulsion by the state of Alabama of its membership list, courts have recognized that the First Amendment protects against this sort of compulsion in this sort of circumstance.

In practice, the Trump-Koch alliance has been extraordinarily productive, and the alliance is the odds on favorite to win the battle to put Kavanaugh on the Supreme Court, where he is likely to cement a conservative majority for the foreseeable future.

For two decades, key Democrats have argued that as the party of the multiracial, multiethnic rising American electorate — and the political home of single women and younger voters — they have the demographic wind at their backs. But time and again, the Republican Party, the de facto party of white America, has surged back.

Looking toward November, the Koch organizations are already committed to attacking incumbent Democratic Senators in Wisconsin, Indiana, Missouri and Florida while looking at their chance of influencing the outcome in as many as 14 other races. In addition, the network plans to support Republican candidates for governor in Nevada, Wisconsin, Illinois, Michigan and Florida, a list that is expected to grow longer as the midterms heat up.

At another level, few politicians in American history have been as resourceful as Trump in ginning up white resentment and focusing the resulting anger directly on Democrats, liberals and minorities. From MS-13 gangs, to kneeling professional football players and the recent death of Mollie Tibbetts, nothing is out of bounds — even the pleas of Tibbetts’s father that Trump stop politicizing her murder.

Despite his liabilities, Trump is determined to press forward in concert with the Kochs on behalf of a besieged Republican Party and an agenda of benefits for corporate entities and the wealthy.

In the 2016 Republican primaries, the party’s voters effectively declared that they were fed up with establishment candidates and demanded a red-meat nominee who would cater to “working white America.”

Despite their misgivings, the Kochs — and Republican politicians like Paul Ryan and Mitch McConnell — owe Trump a great deal. And because this is a political form of symbiosis, he owes them just as much.

What will this alliance cost each partner? What are the possible consequences of their nonaggression pact? Everything temporary always looks permanent. The only certainty is that the equilibrium is bound to shift left or right. It can’t stay like this forever.

An earlier version of this column misstated the size of the tax cut that was enacted by Congress in December; it was $1.5 trillion, not $1.5 billion.

Thomas B. Edsall has been a contributor to The Times Opinion section since 2011. His column on strategic and demographic trends in American politics appears every Thursday. He previously covered politics for The Washington Post. @edsall